Question

How to find the area of the triangle whose vertices are (0,0) , (3,0), (0,2)

Answer 1

$\blue{\bold{\underline{\underline{Answer:}}}}$

$\green{\tt{\therefore{Area\:of\:triangle=3\:units^{2}}}}$

$\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

$\green{\underline \bold{Given :}} \\ \tt: \implies vertices \: of \: triangle = (0,0),(3,0)\:and\:(0,2) \\ \\ \red{\underline \bold{To \: Find :}} \\ \tt: \implies Area \: of \: triangle =?$

• According to given question :

$\bold{As \: we \: know \: that} \\ \tt: \implies Area \: of \: triangle = \frac{1}{2} \bigg[x_{1}( y_{2} - y_{3}) + x_{2}( y_{3} - y_{1}) + x_{3}( y_{1} - y_{2})\bigg] \\ \\ \tt: \implies Area \: of \: triangle = \frac{1}{2} \bigg[0(0 - 2) + 3(2 - 0) + 0(0 - 0)\bigg] \\ \\ \tt: \implies Area \: of \: triangle = \frac{1}{2} (0 + 3 \times 2 + 0) \\ \\ \tt: \implies Area \: of \: triangle = \frac{1}{2} (6) \\ \\ \green{\tt: \implies Area \: of \: triangle =3 \: units^{2} }\\\\ \blue{\boxed{ \bold{Some \: related \: formula}}} \\ \orange{ \tt \circ \: \: Distance \: formula = \sqrt{ (x_{2} - x_{1})^{2} + (y_{2} - y_{1})^{2} } } \\ \\ \orange{ \tt \circ \: \: Mid \: point \: formula = \frac{ x_{1} + x_{2} }{2} .\frac{ y_{1} + y_{2} }{2}} \\ \\ \orange{ \tt \circ \: \:Section \: formula = \frac{ mx_{2} + nx_{1} }{m + n} }$